June 23, 2011

## The evolution of vision

Recently, Scientific American came out with an article on the history of the evolution of the eye.  Intelligent Design proponents have used that as the basis for renewing old creationist arguments against the idea that the eye evolved.  See here and here.

The Scientific American article is about the evolution of the physical eye, rather than about the evolution of the visual system.  The ID response, too, is about the physical eye.  But it is the usual argument about irreducible complexity.  According to that argument, a change in the physical eye would have to have a corresponding change in the entire visual processing system, before there could be any benefit.  And this is part of why ID proponents and creationists see it as irreducibly complex.

June 23, 2011

## Geometry and logic (2)

In my first post for this series, I mentioned “geometric method,” but I did not explain what I mean when I use that expression.  That is what I want to discuss today.  In doing so, I widen our horizons beyond mathematics, and look at how we use geometric methods in the real world.  In particular, I shall discuss its epistemic significance.

June 22, 2011

## Geometry and logic

While preparing to write this post, I did a google search for “geometric method.”  Many of the results of the search were about logic rather than about geometry as, for example, in Spinoza’s geometric method.  In a way that makes sense, for Euclid’s geometry is famous for its use of self-evident axioms.  However, that is not at all what I think of when I think about geometry and geometric method.

The way logic is used in geometry is very different from the way it is used in ordinary propositional logic.  And that is what I mainly want to discuss here.

June 9, 2011

## A mathematician’s take on phenomena

This is, in part, a response to the recent John Wilkins blog post “More on phenomena.”  It is based on my ideas on human cognition and human perception.  Unavoidably, this will be a tad mathematical.  However, I will avoid getting into technical terminology to the extent that I can, though I’ll give enough as hints to the mathematical literature for those who want to pursue the underlying mathematics.

Think of the world as a topological space, call it W.  (For the mathematicians, I am taking W to be a normal Hausdorff space).  Because W is a topological space, we can think about continuous functions over that space.  So for a point x in W, and a continuous function f, there is a value f(x) for that function at that point.  For technical reasons, mathematicians usually take their continuous functions to have values that are complex numbers.  However, I suggest thinking about them as functions with values that are real numbers.

If we look at this in terms of science, then we can think of the function f as a method of measuring, and we can think of the value f(x) as an actual measurement (or as a datum).

June 6, 2011